Why can quantities with different units be multiplied or divided?

Answer 1

well because You can always multiply and divide units by a number. For example, suppose you have four chairs but find that you need twice as many for a party. Here's how you represent this idea in math:

4 chairs 2 = 8 chairs

Similarly, suppose you have 20 cherries and want to split them among four people. Here's how you represent this idea:

20 cherries 4 = 5 cherries

But you have to be careful when multiplying or dividing units by units. For example:

2 apples 3 apples = ? WRONG!

12 hats 6 hats = ? WRONG!

Neither of these equations makes any sense. In these cases, multiplying or dividing by units is meaningless.

In many cases, however, multiplying and dividing units is okay. For example, multiplying units of length(such as inches, miles, or meters) results in square units:

3 inches 3 inches = 9 square inches

10 miles 5 miles = 50 square miles

100 meters 200 meters = 20,000 square meters

Similarly, here are some examples of when dividing units makes sense:

12 slices of Pizza 4 people = 3 slices of pizza/person

140 miles 2 hours = 70 miles/hour

In these cases, you read the fraction slash (/) as per: slices of pizza per person or miles per hour.